Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+6y &= -6 \\ -2x-7y &= -3\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = 7y-3$ Divide both sides by $-2$ to isolate $x$ $x = {-\dfrac{7}{2}y + \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $-6({-\dfrac{7}{2}y + \dfrac{3}{2}}) + 6y = -6$ $21y - 9 + 6y = -6$ Simplify by combining terms, then solve for $y$ $27y - 9 = -6$ $27y = 3$ $y = \dfrac{1}{9}$ Substitute $\dfrac{1}{9}$ for $y$ in the top equation. $-6x+6( \dfrac{1}{9}) = -6$ $-6x+\dfrac{2}{3} = -6$ $-6x = -\dfrac{20}{3}$ $x = \dfrac{10}{9}$ The solution is $\enspace x = \dfrac{10}{9}, \enspace y = \dfrac{1}{9}$.